Energy Cycles at Constant Volume


Consider the energy cycle depicted in the P-V diagram below with 2 stages at constant volume and 2 stages at constant pressure

    Initial state 1 a fixed mass of gas volume V pressure P and temperature T1


    Stage 1-2     the gas is heated at constant volume to temperature T2

                        raising pressure to P′               Heat input Cv (T2 - T1)


    Stage 2-3     the gas is heated at constant pressure to temperature T3

                        and volume V′                        Heat input Cp (T3 - T2)

    Stage 3-4     work done by gas at constant volume so that pressure

                        falls to P and temperature fall to T4

                        There is no heat input Q = DU + W = 0

                        work done by the gas Cv (T3 T4)

    Stage 4-1     heat taken out of the gas into energy sink at constant

                        pressure so that volume returns to V and temperature to T1


                        Efficiency     =     useful work achieved

                                                       total heat input



                                            =              Cv (T3 - T4)


                                                  Cv (T2 - T1) + Cp(T3 - T2)


Now consider the energy cycle portrayed approximating towards a constant volume heat engine

                    As      V′    V       T4    T1    T3   T2   and     (T3 T2)      0

                    Efficiency                 Cv (T2 - T1)          100%


                                                       Cv (T2 - T1)


If an energy cycle can be devised with the entire heat input and extraction of work at constant volume it will have a maximum theoretical efficiency of 100%.



                                                                                                                    [Convector Generator]